Cambridge City Council voted Monday night to approve a controversial plan for Google Inc. to increase its Kendall Square office in an expansion that would halve a public rooftop garden.

The proposal sparked outcry late last month when it was presented to city council by Boston Properties Inc., Google’s landlord, after some councilors and residents said they were surprised by losses to the park, which sits atop of a Kendall Square parking garage and is protected by an open-space covenant.

Boston Properties returned to city council Monday with a slightly revised proposal that includes bumping up the amount of new park space the developer will construct in exchange for reducing the garden and pledging to $2 million to design and construct that green space.

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“This is a step in a process,” said Steve Vinter, head of Google’s Cambridge office, after the council’s 7 to 2 vote in favor of the plan. “Growing is a thing that takes time and we are really appreciative of the work done by the community and the council.”

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Vinter said previously that Google needs to expand in Cambridge to accommodate a growing workforce. Last night, he put Google’s local head count was about 800, growing from 40 people just five years ago. The search engine giant acquired ITA Software Inc., another Kendall Square tech company with about 500 employees, in 2010.

The expansion plan includes the construction of two glass-wall connectors that will link Four, Five, and Three Cambridge Center. Boston Properties said construction should begin later this year with an expected completion date of mid-2013.

The expansion will add about 40,000 square feet between the buildings, and allow Google to spread out across 300,000 square feet of office space.

The controversy was focused largely on the connector between Four and Five Cambridge Center because it sits on top of a parking garage and will lop off 18,000 square feet from the rooftop garden, which dates back to 1983. Boston Properties needed council approval to build on top of the public park.

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“It is an oasis, an Eden, a marvel, something that Boston Properties should be incredibly proud of because of the stellar job they did and do creating and maintaining it. Destroying it should be the last thing on their minds,” said Heather Hoffman, a Cambridge resident and member of the East Cambridge Planning Team, who spoke out against the expansion.

The East Cambridge planning group, which met Boston Property and Google officials last week to discuss the proposal, originally voted against supporting the proposal in its current form, and instead offered an alternative plan. It suggested that Boston Properties attempt to extend the rooftop garden onto an adjacent building instead of developing another ground-level park nearby.

But on Monday night the East Cambridge group said its board members opted to back the revised plan, which Boston Properties submitted to the City of Cambridge last Friday.

Charles Marquardt, a member of the executive board of the East Cambridge Planning Team, said his group would still like to see more of a commitment from Boston Properties to build residential units in the neighborhood in the near future.

As part of the revised plan, Boston Properties said it would present plans for about 180 residential units a year after the additions to Google are completed.